1. Field of the Invention
This invention relates to extruders of the type which employ single screws that use chaotic mixing to generate substantially better distributive mixing. Such structures of this type, generally, stretch and fold material lines repeatedly such that interfacial areas between material elements increase exponentially and heat/mass transfers are greatly enhanced.
2. Description of the Related Art
Single screw extruders are widely used in the plastics industry as mixers and pumps. The simplest design consists of a screw which rotates inside a dose fitting cylindrical barrel. The screw, typically, includes a feed section, a transition section, and a metering section. Virtually all studies of single screw extruders are based on the unwound representation of the screw channel. The relative motion of the screw and the barrel appears as a plate which moves diagonally on top of the channel (see FIG. 1) in the direction of arrow V.
The fluid flow in the channel can be decomposed into two components, namely, a cross flow in the x.sub.1 -x.sub.2 plane and an axial flow in the x.sub.3 -direction. The axial flow pumps the materials forward and the cross flow mixes them. However, the mixing in such a conventional screw is poor.
With respect to FIG. 2, typically, a mixing section such as a Maddock mixing section, a pin mixing section (see also FIG. 3d), a pineapple mixing section, a blister ring, and so on, is added to the screw to increase its dispersive and/or distributive mixing capability. However, these mixing sections are relatively short compared to the length of the screw. It is to be understood that the arrows in FIG. 3 indicate the location of the channel in unit diameter from the shank.
The screw section responsible for mixing is typically characterized by its closeness to the outer barrel to generate the high shear stress required for a dispersive mixing (e.g., Maddock section and blister ring), or by a large number of small units affixed on the root of the screw for a distributive mixing (e.g. pin and pineapple mixing sections).
A different kind of mixing screw, such as barrier screws (see FIGS. 3a and 3b) is designed based on the solid-melt distribution as it is conveyed down the metering section. The barrier screw has two channels, used to separate melt from solid, of varying width separated by an undercut barrier flight. The width of the channel is proportional to the amount of solid or melt. Initially, as pellets start to melt, the melt pool is pushed into the narrow melt channel. The melt channel grows larger as more melt is collected. The Barr ET screws (namely, a Barr ET Barrier screw (manufactured by Robert Barr Incorporated of Virginia Beach, Va.) is claimed to have 30 to 50% better melting rate through mixing of pellets with fresh melt.
Double wave screws are also used. A conventional double wave screw (as shown in FIG. 3c) such as that produced by the HPM Corporation of Mount Gilead, Ohio has two equal width channels separated by an undercut barrier flight. The roots of each channel go up and down like a wave. The channel depth on one is shallow while the channel across is deep. This continually reverses and forces melted polymer back and forth across the barrier. The material in the channel is alternately subjected to high then low shear. Usually these double wave mixing sections are located in the metering section where the plastic has already been melted and run along about 3 to 4 waves. Again, while these double wave screws have increased the mixing, it would still be desirable to increase the mixing even further.
Recent work indicate that time-periodic change of geometry in a 3-dimensional continuous flow can produce chaos in mixing. The spatial-perodicity is aimed to perturb the existing streamline, to induce sustained material re-orientation, and thus, folding. Time integration of the stretching rate of a material line subjected to such periodic re-orientation results in a positive number, also known as a Lyapunov exponent (besides stretching and folding, positive Lyapunov exponent is another signature of chaos).
Also, a two-dimensional Hamiltonian system with periodic time forcing can produce chaos. For example, a cavity (like a deep aquarium tank) filled with a viscous fluid with any one of its walls in motion (for example, the top wall moving left to right) is a 2-dimensional Hamiltonian system. If one wall (for example, the top wall) is put in motion for a duration of time (t.sub.1) and then stopped, then another wall (for example, the bottom wall) is put in motion for a duration of time (t.sub.2) and then stopped, then chaos is possible.
Finally, periodic geometric change, instead of periodic time forcing can also produce chaos. As with the cavity example above, if the top wall is moved and the geometry of the rest of the cavity is changed, this will produce chaotic mixing. An example of changing the geometry would be to use baffle inserts. It should be noted however, that neither the periodic time forcing or the periodic geometric change of more than 5 continuous periods or repeat units has been applied to existing screw configurations. Therefore, a more advantageous screw would then be presented if such chaotic mixing could be applied to existing screws.
It is apparent from the above there exists a need in the art for an extruder which is capable of distributive mixing, and which at least equals the mixing characteristics of known screws, but which at the same time is also capable of excellent heat/mass transfer through the use of chaotic mixing. It is a purpose of this invention to fulfil this and other needs in the art in a manner more apparent to the skilled artisan once given the following disclosure.